Iq test if i have two tetrahedral pyramids

  • Thread starter datatec
  • Start date
  • Tags
    Iq Test
In summary, the minimum number of balls needed to make a larger pyramid by combining two equally sized tetrahedral pyramids is 20. To make a larger pyramid with two different sized pyramids, the minimum number of balls needed is also 20, with one pyramid having 4 balls and the other having 10 balls. However, if the pyramids must be tetrahedral in shape, there is no integer solution for this problem.
  • #1
datatec
17
0
this one i got from an iq test

if i have two tetrahedral pyramids of equal sizes made of golf balls and I combine them (presuming every ball is used) the minumum amount of balls needed would be 20 to make one larger pyramid. What would the minimum be should the two smaller pyramids be different sizes? :wink:
 
Physics news on Phys.org
  • #2
Select to see...:-)

The same 20 balls (you may have 2 pyramids made of 4 and 10 balls).
 
Last edited:
  • #3
Nope

You need to use all the balls. In your case you have six remaining.
 
  • #4
I hope that answer is not some giant number, and that there will be a solution within 1000...but I'm having doubts.
 
  • #5
I don't think I understand the question correctly.
You said if you combine the number of balls from two equally sized tetrahedral pyramids and add 20, then you have the number of balls needed to make a pyramid one size larger.
The number of balls needed for a pyramid of size n is:
[tex]\sum_{i=0}^ni^2=\frac{1}{6}n(n+1)(2n+1)[/tex]
so the equation to solve is:
[tex]2\frac{1}{6}n(n+1)(2n+1)+20=\frac{1}{6}(n+1)(n+2)(2n+2)[/tex]
to find the size of the smaller pyramids.
But it has no integer solutions...

Possibly, my picture of making pyramids with golfballs is wrong.
Stacking them like this will not make them tetrahedral, but I don't see any other way to do it.
 
  • #6
Galileo said:
I don't think I understand the question correctly.
You said if you combine the number of balls from two equally sized tetrahedral pyramids and add 20, then you have the number of balls needed to make a pyramid one size larger.
The number of balls needed for a pyramid of size n is:
[tex]\sum_{i=0}^ni^2=\frac{1}{6}n(n+1)(2n+1)[/tex]
so the equation to solve is:
[tex]2\frac{1}{6}n(n+1)(2n+1)+20=\frac{1}{6}(n+1)(n+2)(2n+2)[/tex]
to find the size of the smaller pyramids.
But it has no integer solutions...

Possibly, my picture of making pyramids with golfballs is wrong.
Stacking them like this will not make them tetrahedral, but I don't see any other way to do it.

The question is simply, "What 2 dissimilar tetrahdra (built from balls) can be combined to make a new tetrahedron, using exactly the number of balls contained in the smaller ones ?"

The case of 20 balls would be a solution were this question lacking the word 'dissimilar'. It has nothing to do with the current question.

Next, a tetrahedral number of height n, is the sum of the first n triangular numbers, and so, should be given by the sum

[tex]\sum_{i=0}^n{i(i+1)/2}=\frac{1}{12}n(n+1)(2n+1) + \frac {n(n+1)}{4}[/tex]

Triangular numbers are : 1,3,6,10,15,21,28,...
Tetrahedral numbers are : 1,4,10,20,35,56,84,120,...

We are looking for 2 different Tet. Numbers that add to give a third one.
 
  • #7
Gokul43201 said:
Next, a tetrahedral number of height n, is the sum of the first n triangular numbers, and so, should be given by the sum

Oh yeah... a tetrahedron has 4 sides.
I can' t count. :redface:
 
  • #8
In white.
751966976
 
  • #9
Wrong Again

I´m afraid you're wrong.
Clue in white:

The answer is below 1000
 
  • #10
Ahh, i was doing half of an octahedron, not a tetrahedron.

ANSWER :
680 balls, by a height of 14 and a height of 8 TH's to make a height of 15 TH.
 

FAQ: Iq test if i have two tetrahedral pyramids

1. What is the purpose of an IQ test?

The purpose of an IQ test is to measure a person's cognitive abilities, including their problem-solving skills, memory, and reasoning abilities. It is used to assess a person's overall intelligence and potential for success in various areas.

2. How is an IQ test scored?

IQ tests are scored by comparing an individual's performance to that of others in their age group. The average score is set at 100, and scores above or below this indicate above or below average intelligence.

3. What are the two tetrahedral pyramids in an IQ test?

The two tetrahedral pyramids in an IQ test refer to the two types of questions commonly used in IQ tests: verbal and non-verbal. Verbal questions assess a person's language and comprehension skills, while non-verbal questions test their spatial and visual reasoning abilities.

4. How do tetrahedral pyramids relate to IQ tests?

Tetrahedral pyramids are used in IQ tests to represent different types of questions. The shape of the pyramid symbolizes the different cognitive abilities that are being assessed, and the two pyramids together represent the comprehensive nature of an IQ test.

5. Can an IQ test accurately measure intelligence?

An IQ test can provide a general indication of a person's cognitive abilities, but it is not a comprehensive measure of intelligence. Factors such as cultural background, education, and life experiences can also impact a person's intelligence and may not be reflected in their IQ test score.

Back
Top